triangle bisectors 5.1 (part 2). swbat construct perpendicular bisectors and angle bisectors of...

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Triangle Bisectors 5.1 (Part 2)

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concurrent point of concurrency circumcenter circumscribed incenter inscribed Vocabulary

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Page 1: Triangle Bisectors 5.1 (Part 2). SWBAT Construct perpendicular bisectors and angle bisectors of triangles…

Triangle Bisectors5.1 (Part 2)

Page 2: Triangle Bisectors 5.1 (Part 2). SWBAT Construct perpendicular bisectors and angle bisectors of triangles…

SWBAT• Construct perpendicular bisectors

and angle bisectors of triangles• Apply properties of perpendicular

bisectors and angle bisectors of triangles

Page 3: Triangle Bisectors 5.1 (Part 2). SWBAT Construct perpendicular bisectors and angle bisectors of triangles…

•concurrent•point of concurrency

•circumcenter•circumscribed

• incenter• inscribed

Vocabulary

Page 4: Triangle Bisectors 5.1 (Part 2). SWBAT Construct perpendicular bisectors and angle bisectors of triangles…

When three or more lines intersect at one point, the lines are said to be concurrent

The point of concurrency is the point where

the lines intersect

Page 5: Triangle Bisectors 5.1 (Part 2). SWBAT Construct perpendicular bisectors and angle bisectors of triangles…

5

Since a Triangle has three vertices...

It has three Angle Bisectors.

What did you notice about the Angle Bisectors of the Triangles?

5

Page 6: Triangle Bisectors 5.1 (Part 2). SWBAT Construct perpendicular bisectors and angle bisectors of triangles…

Angle bisectors start at a vertexAngle bisectors start at a vertexand and bisect the angle.bisect the angle.

IncenterIncenter

Angle Bisectors

The Incenter is the Point of Concurrency of the Angle Bisectors

Page 7: Triangle Bisectors 5.1 (Part 2). SWBAT Construct perpendicular bisectors and angle bisectors of triangles…

The incenter is always inside the triangle.

Page 8: Triangle Bisectors 5.1 (Part 2). SWBAT Construct perpendicular bisectors and angle bisectors of triangles…

Any point on an angle bisector is Any point on an angle bisector is equidistant from the sides of the angle equidistant from the sides of the angle

Page 9: Triangle Bisectors 5.1 (Part 2). SWBAT Construct perpendicular bisectors and angle bisectors of triangles…

This makes the This makes the IncenterIncenterequidistant from all 3 sidesequidistant from all 3 sides

Page 10: Triangle Bisectors 5.1 (Part 2). SWBAT Construct perpendicular bisectors and angle bisectors of triangles…

The incenter is the center of the triangle’s inscribed circle. A circle inscribed in a polygon intersects each line that contains a side of the polygon at exactly one point.

Page 11: Triangle Bisectors 5.1 (Part 2). SWBAT Construct perpendicular bisectors and angle bisectors of triangles…

Since a Triangle has three sides...

It has three Perpendicular Bisectors.

What did you notice about the Perpendicular Bisectors of the

Triangles?

Page 12: Triangle Bisectors 5.1 (Part 2). SWBAT Construct perpendicular bisectors and angle bisectors of triangles…

A Perpendicular bisector of a side formsA Perpendicular bisector of a side forms a a 90° angle90° angle and bisects the sideand bisects the side..

CircumcenterCircumcenter

Perpendicular Bisectors

The Circumcenter is the Point of Concurrency of the Perpendicular Bisectors

Page 13: Triangle Bisectors 5.1 (Part 2). SWBAT Construct perpendicular bisectors and angle bisectors of triangles…

The circumcenter can be inside the triangle, outside the triangle, or on the triangle.

Page 14: Triangle Bisectors 5.1 (Part 2). SWBAT Construct perpendicular bisectors and angle bisectors of triangles…

Recall:Recall: Any point on the Any point on the perpendicular bisectorperpendicular bisector

of a segment is equidistant from theof a segment is equidistant from theendpoints of the segment.endpoints of the segment.

AA

BB

CC DD

AB is the AB is the perpendicularperpendicularbisector of CDbisector of CD

Page 15: Triangle Bisectors 5.1 (Part 2). SWBAT Construct perpendicular bisectors and angle bisectors of triangles…

This makes the This makes the CircumcenterCircumcenterequidistant from the 3 verticesequidistant from the 3 vertices

Page 16: Triangle Bisectors 5.1 (Part 2). SWBAT Construct perpendicular bisectors and angle bisectors of triangles…

The circumcenter of ΔABC is the center of its circumscribed circle. A circle that contains all the vertices of a polygon is circumscribed about the polygon.

Page 17: Triangle Bisectors 5.1 (Part 2). SWBAT Construct perpendicular bisectors and angle bisectors of triangles…

Survival TrainingSurvival TrainingYou’re Stranded On A Triangular You’re Stranded On A Triangular

Shaped Island. The Rescue Ship CanShaped Island. The Rescue Ship CanOnly Dock On One Side Of The Island Only Dock On One Side Of The Island

But You Don’t Know Which Side. At But You Don’t Know Which Side. At Which Point Of Concurrency Would Which Point Of Concurrency Would

You Set Up Camp So You Are An You Set Up Camp So You Are An EqualEqual Distance From All 3 Sides?Distance From All 3 Sides?

INCENTERINCENTER

Page 18: Triangle Bisectors 5.1 (Part 2). SWBAT Construct perpendicular bisectors and angle bisectors of triangles…

What If The Ship Could OnlyWhat If The Ship Could OnlyDock At One Of The Vertices? Dock At One Of The Vertices? Would You Change The Would You Change The Location Of Your Camp ?Location Of Your Camp ?If So, Where?If So, Where?

YESYES CIRCUMCENTERCIRCUMCENTER